So why did Microsoft and Sony opt for relatively weak cpus by AMD instead of chips by Intel? A lot of products nowadays have Intel's chip as their cpus. In Microsoft's case, the Surface runs with i3, i5, and i7. Perhaps they will use profits from this gen to create powerful hardware next generation? Phones, tablets, and other stuff can be crazy expensive but gaming consoles can't?
Both the XB1 and PS4 use APUs. CPU and GPU on s single die. If they went with Intel, they couldn't do this (unless they wanted very poor GPU performance).
An APU keeps manufacturing costs down, uses less power compared to discrete chips, allows for more control over cost reduction in the future, and ties them into a single vendor.
Consoles are all about bang for buck, and the AMD APU gives the best performance/cost. It's no coincidence that both MS and Sony went to market to design their next gen consoles, and independently both came out with effectively the same architecture from the same vendor.